Fractured reservoirs are an extreme kind of heterogeneous reservoirs, with two contrasted media, a matrix medium containing most of the oil in place and having a low permeability, and a fracture medium usually representing less than 1% of the oil in place and being highly conductive. The fracture medium itself may be complex, with different fracture sets characterized by respective fracture density, length, orientation, tilt and aperture. 3D images of fractured reservoirs are not directly usable as a reservoir simulation input. Representing the fracture network in reservoir flow simulators was long considered as unrealistic because the network configuration is partially unknown and because of the numerical limitations linked to the juxtaposition of numerous cells with extremely-contrasted sizes and properties. Hence, a simplified but realistic modeling of such media remains a concern for reservoir engineers.
The "dual-porosity approach", as taught for example by Warren, J. E. et al "The Behavior of Naturally Fractured Reservoirs", SPE Journal (September 1963), 245-255, is well-known in the art for interpreting the single-phase flow behavior observed when testing a fractured reservoir. According to this basic model, any elementary volume of the fractured reservoir is modelled as an array of identical parallelepipedic blocks limited by an orthogonal system of continuous uniform fractures oriented along one of the three main directions of flow. Fluid flow at the reservoir scale occurs through the fracture medium only, and locally fluid exchanges occur between fractures and matrix blocks.
Numerous fractured reservoir simulators have been developed using such a model, with specific improvements concerning the modeling of matrix-fracture flow exchanges governed by capillary, gravitational, viscous forces and compositional mechanisms, and consideration of matrix to matrix flow exchanges (dual permeability dual-porosity simulators). Various examples of prior art techniques are referred to in the following references:
Thomas, L. K. et al: "Fractured Reservoir Simulation," SPE Journal (February 1983) 42-54. PA1 Quandalle, P. et al: "Typical Features of a New Multipurpose Reservoir Simulator", SPE 16007 presented at the 9th SPE Symposium on Reservoir Simulation held in San Antonio, Tex., Feb. 1-4, 1987; and PA1 Coats, K. H.: "Implicit Compositional Simulation of Single-Porosity and Dual-Porosity Reservoirs," paper SPE 18427 presented at the SPE Symposium on Reservoir Simulation held in Houston, Tex., Feb. 6-8, 1989. PA1 Bourbiaux, B. et al: "Experimental Study of Cocurrent and Countercurrent Flows in Natural Porous Media," SPE Reservoir Engineering (August 1990) 361-368. PA1 Cuiec, L., et al.: "Oil Recovery by Imbibition in Low-Permeability Chalk," SPE Formation Evaluation (September 1994) 200-208. PA1 forming an image of at least two dimensions of the geological medium as an array of pixels, and associating with each pixel of the array a particular initial value for said function, PA1 step by step determining a value to assign for the physical transfer function at each pixel of said array, by reference to values of the function assigned to neighboring pixels of the image; and PA1 determining a physical property of the transposed or equivalent medium by identifying values of the transfer function known for the (simplified) transposed medium with the step by step determined value of the transfer function for the original medium. PA1 forming an image of at least two dimensions of the actual medium as an array of pixels; PA1 determining for each pixel the minimum distance separating the pixel from the nearest fracture; PA1 forming a distribution of numbers of pixel versus minimum distances to the fracture medium, and determining therefrom the recovery function (R) of said set of blocks and PA1 determining dimensions (a,b) of the equivalent regular blocks of the set from the recovery function (R) and from the recovery function (Req) of the equivalent (using e.g. a procedure of identification of said recovery functions).
A problem met by reservoir engineers is to parameterize this basic model in order to obtain reliable flow predictions. In particular, the equivalent fracture permeabilities, as well as the size of matrix blocks, have to be known for each cell of the flow simulator. Whereas matrix permeability can be estimated from cores, the permeabilities of the fracture network contained in the cell, i.e. the equivalent fracture permeabilities, cannot be estimated in a simple way and require taking the geometry and properties of the actual fracture network into account. A method of determining the equivalent fracture permeabilities of a fracture network is disclosed in the parallel patent application EN. 96/16330.
There is known a reference procedure for determining the dimensions a, b of each block of a section crossed by a regular grid of fractures Feq which is equivalent to the section of a natural fractured multi-layered medium crossed by a fracture network FN along a datum plane parallel with the layers (commonly horizontal or substantially horizontal plane). For each layer of the fractured rock volume studied (FIG. 1), the "horizontal" dimensions a, b of the blocks of the equivalent section are determined iteratively by computing and comparing the oil recovery functions versus time R(t) and Req(t) respectively in the real section RE of the fractured rock volume studied and in the section EQ of equally-sized "sugar lumps" equivalent to the distribution of real blocks. This conventional method requires a single-porosity multiphase flow simulator discretizing matrix blocks and fractures in such a way that the recovery curves can be compared. Such a procedure is very costly as the discretization of the real section may involve a very high number of cells. Actually, the real shape of blocks must be represented using thin fracture cells along the boundaries of each block. The matrix must also be discretized with a sufficient number of cells to obtain an accurate block-fracture imbibition transfer function.
Different prior art techniques in the field can be found, for example, in:
However no use of the specific imbibition features has yet been made to find dimensions of the equivalent block in dual-porosity models. So reservoir engineers lack of a systematic tool for computing dimensions of a parallelepipedical block which is equivalent for multiphase flows to actual distribution of blocks in each fractured reservoir zone.
Techniques for integrating natural fracturing data into fractured reservoir models are also known in the art. Fracturing data are mainly of a geometric nature and include measurements of the density, length, azimuth and tilt of fracture planes observed either on outcrops, mine drifts, or cores or inferred from well logging. Different fracture sets can be differentiated and characterized by different statistical distributions of their fracture attributes. Once the fracturing patterns have been characterized, numerical networks of those fracture sets can be generated using a stochastic process respecting the statistical distributions of fracture parameters. Such processes are disclosed, for example, in patents FR-A-2, 725, 814, 2, 725, 794 or 2, 733, 073 of the applicant.